Authors: Šešelja, Branimir
Stepanović, Vanja
Tepavčević, Andreja 
Title: Representation of lattices by fuzzy weak congruence relations
Journal: Fuzzy Sets and Systems
Volume: 260
First page: 97
Last page: 109
Issue Date: 1-Jan-2015
Rank: M21a
ISSN: 0165-0114
DOI: 10.1016/j.fss.2014.05.009
Fuzzy (lattice valued) weak congruences of abstract algebras are investigated. For an algebra, the family of all such fuzzy relations is a complete lattice; its structure and cut properties are investigated and fully described. These fuzzy weak congruences are applied in representation of complete and algebraic lattices. A wider class of lattices can be represented in such a fuzzy framework, than in classical algebra. We prove that there is a straightforward representation of any complete lattice, using it as a co-domain. In a more general case, it is proved that several subdirect powers of lattices are also representable by fuzzy weak congruences.
Keywords: Algebra | Complete lattice | Fuzzy algebra | Fuzzy relations | Fuzzy weak congruence
Publisher: Elsevier
Project: Development of methods of computation and information processing: theory and applications 
Provincial Secretariat for Science and Technological Development, Autonomous Province of Vojvodina, Grant “Ordered structures and applications”

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